Lesson 12: Solutions to Inequalities in One Variable (Alg1.2.19)

Autor:Brenda Jiménez, IM Algebra 1, Geometry, Algebra 2 , GeoGebra Classroom Activities

Find a Value, Any Value

Write some solutions to the inequality . Be prepared to explain what makes a value a solution to this inequality.

Write one solution to the inequality . Be prepared to explain your reasoning.

Part-Time Work

To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-time jobs: working in the guest-services department at a hotel and waiting tables at a popular restaurant.

The job at the hotel pays $18 an hour and offers $33 in transportation allowance per month.
The job at the restaurant pays $7.50 an hour plus tips. The entire waitstaff typically collects about $50 in tips each hour. Tips are divided equally among the 4 waitstaff members who share a shift.

The equation

represents a possible constraint about a situation. Solve the equation and check your solution.

Here is a graph on a number line. Put a scale on the number line so that the point marked with a circle represents the solution to the equation.

Does one job pay better if:

The student works fewer hours than the solution you found earlier? If so, which job? Be prepared to explain or show how you know.

The student works more hours than the solution you found earlier? If so, which job? Be prepared to explain or show how you know.

Here are two inequalities and two graphs that represent the solutions to the inequalities.

Inequality 1:

Inequality 2:

Match each inequality with a graph that shows its solution. Be prepared to explain or show how you know.

More practice?

What is the solution to the inequality ? Be prepared to explain how you know.

Graph the solution to the inequality on the number line.

For each statement:

Use a number line to show which values satisfy the inequality. Express the statement symbolically with an inequality. 1. The elevator can lift up to 1,200 pounds. Let x represent the weight being lifted by the elevator.

2. Over the course of the senator's term, her approval rating was always around 53% ranging 3% above or below that value. Let x represent the senator’s approval rating.

3. There's a minimum of 3 years of experience required. Let x represent the years of experience a candidate has.